On improving the determination of the neutron distribution in a heavy spin-0 nucleus

As a theorists' guide to future experiments, we investigate the possibility of improving the determination of the rms neutron radius in a heavy spin-0 nucleus by combining measurements of the left-right asymmetry in parity violating electron scattering at two different momentum transfers. We estimate the level of constraint on R_n ≡ ⟨r²⟩^1/2_n for spin-0 nuclei in a nuclear model independent analysis in both plane wave and Coulomb distorted calculations. We find that experiments at two different kinematics reduce the need to make theoretical arguments about present uncertainties in the shape of the spatial neutron distribution compared to a single experiment with the same total beam time. We estimate that the rms neutron radius in ²⁰⁸Pb can be constrained at about the 1% level, without requiring significant theoretical nuclear model assumptions.